Massless finite and infinite spin representations of Poincar\'{e} group in six dimensions

TL;DR

This paper classifies massless irreducible representations of the Poincaré group in six dimensions, identifying parameters that define finite and infinite spin representations through Casimir operators.

Contribution

It provides a detailed construction of Casimir operators and characterizes the parameters defining finite and infinite spin representations in six-dimensional spacetime.

Findings

Finite spin representations are characterized by two integers or half-integers.

Infinite spin representations depend on a real parameter and an integer or half-integer.

Eigenvalues of Casimir operators are explicitly calculated.

Abstract

We study the massless irreducible representations of the Poincar\'{e} group in the six-dimensional Minkowski space. The Casimir operators are constructed and their eigenvalues are found. It is shown that the finite spin (helicity) representation is defined by two integer or half-integer numbers while the infinite spin representation is defined by the real parameter $\mu^2$ and one integer or half-integer number.